Optimal matched linear filter for filament detection. Top panel: variance for filaments at redshift z = 0.55. For a given survey with intrinsic ellipticity scatter of σϵ = 0.4, different core radii hc and different galaxy number densities n are plotted. Continuous lines refer to a filter with length L = 10, arcmin while dashed lines refer to L = 20 arcmin. Bottom panel: expected filter response for a filament located at z = 0.55, with a major axis position angle of θ = 30 degrees, a maximum convergence of κ0 = 0.02, and a scale radius of hc = 0.25 Mpc/h. The filter was truncated with an inner cutoff of 2.5 arcmin and two different outer cutoffs of 5 arcmin and 10 arcmin.
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